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I don't know if any of these are the BEST way, but rather than leave this question unanswered, here are the different ways I've found:

Questing and mob-killing in Moria will generate reputation items over time, that can be traded in for reputation.

There are a bunch of assorted quests in Moria that give IGG reputation.

There are six crafting quest dailies at three different locations that can be used to generate a lot of crafting resources (if you're set to the right ones) as well as about 1400 Guards reputation points each. (and 700 Miner reputation points as well) That's ~8400 a day, which will take you from nothing to Kindred in a little over 10 days, without having to do anything else.